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http://dx.doi.org/10.12989/sem.2015.55.2.281

Non-linear transverse vibrations of tensioned nanobeams using nonlocal beam theory  

Bagdatli, Suleyman M. (Faculty of Engineering, Department of Mechanical Engineering, Celal Bayar University)
Publication Information
Structural Engineering and Mechanics / v.55, no.2, 2015 , pp. 281-298 More about this Journal
Abstract
In this study, nonlinear transverse vibrations of tensioned Euler-Bernoulli nanobeams are studied. The nonlinear equations of motion including stretching of the neutral axis and axial tension are derived using nonlocal beam theory. Forcing and damping effects are included in the equations. Equation of motion is made dimensionless via dimensionless parameters. A perturbation technique, the multiple scale methods is employed for solving the nonlinear problem. Approximate solutions are applied for the equations of motion. Natural frequencies of the nanobeams for the linear problem are found from the first equation of the perturbation series. From nonlinear term of the perturbation series appear as corrections to the linear problem. The effects of the various axial tension parameters and different nonlocal parameters as well as effects of different boundary conditions on the vibrations are determined. Nonlinear frequencies are estimated; amplitude-phase modulation figures are presented for simple-simple and clamped-clamped cases.
Keywords
nanobeam; transverse vibration; axial tension; perturbation method; nonlocal elasticity;
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Times Cited By KSCI : 3  (Citation Analysis)
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